{"id":1399,"date":"2026-05-12T21:47:44","date_gmt":"2026-05-12T21:47:44","guid":{"rendered":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-10\/"},"modified":"2026-05-13T16:59:12","modified_gmt":"2026-05-13T16:59:12","slug":"solution-exercise-10","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/chapter\/solution-exercise-10\/","title":{"raw":"Solution Exercise 10","rendered":"Solution Exercise 10"},"content":{"raw":"
\r\n
\r\n\r\nVariables:<\/strong>\r\n\r\n<\/div>\r\n
\r\n
[latex]r [\/latex]= 150 m<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]Q\\ = \\frac{300\\frac{\\ \\ m^{3}}{d}}{86400\\ \\frac{s}{d}} = 0.00347\\ \\frac{m^{3}}{s}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nMatch points:\r\n\r\n<\/div>\r\n
\r\n\r\n[latex]t[\/latex]\u00a0=\u00a01\u00a0minute (60 seconds)\r\n\r\n<\/div>\r\n
\r\n\r\n[latex]s[\/latex]\u00a0=\u00a01\u00a0meter\r\n\r\n<\/div>\r\n
\r\n\r\nu\u00a0=\u00a00.31\r\n\r\n<\/div>\r\n
\r\n\r\nW(u)\u00a0=\u00a07\r\n\r\n<\/div>\r\n
\r\n\r\nSolve for T<\/em>:\r\n\r\n<\/div>\r\n
\r\n\r\n[latex]s = \\frac{Q}{4\\pi T}W(u)[\/latex] rearrange for [latex]T = \\frac{Q}{4\\pi s}W(u)[\/latex]\r\n\r\n<\/div>\r\n
\r\n\r\n[latex]u\\ = \\frac{r^{2}S}{4Tt}[\/latex] rearrange for [latex]S = \\frac{u\\ 4Tt}{\\ r^{2}}[\/latex]\r\n\r\n<\/div>\r\n
\r\n
[latex]T\\ = \\ \\frac{0.00347\\frac{{\\ \\ m}^{3}}{s}}{4\\ \\ \\pi\\ \\ 1\\ m}\\ (7)\\ = 0.0019\\ \\frac{{\\ \\ m}^{2}}{s}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n
[latex]S = \\ \\frac{0.31\\ (4)\\ 0.0019\\ \\frac{{\\ \\ m}^{2}\\ }{s}\\ 1\\ \\min\\frac{60s\\ }{\\min}}{\\ (150m)^{2}} = 6.4\\ x\\ 10^{- 6}[\/latex]<\/blockquote>\r\n<\/div>\r\n
\r\n\r\nReturn to Exercise\u00a0<\/span><\/a>10<\/u><\/strong>\u2ba5\r\n\r\n<\/div>\r\n
\r\n\r\nReturn to where text linked to Exercise\u00a010<\/strong><\/span><\/a>\u2ba5\r\n\r\n<\/div>\r\n<\/div>","rendered":"
\n
\n

Variables:<\/strong><\/p>\n<\/div>\n

\n

[latex]r[\/latex]= 150 m<\/p><\/blockquote>\n<\/div>\n

\n

[latex]Q\\ = \\frac{300\\frac{\\ \\ m^{3}}{d}}{86400\\ \\frac{s}{d}} = 0.00347\\ \\frac{m^{3}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Match points:<\/p>\n<\/div>\n

\n

[latex]t[\/latex]\u00a0=\u00a01\u00a0minute (60 seconds)<\/p>\n<\/div>\n

\n

[latex]s[\/latex]\u00a0=\u00a01\u00a0meter<\/p>\n<\/div>\n

\n

u\u00a0=\u00a00.31<\/p>\n<\/div>\n

\n

W(u)\u00a0=\u00a07<\/p>\n<\/div>\n

\n

Solve for T<\/em>:<\/p>\n<\/div>\n

\n

[latex]s = \\frac{Q}{4\\pi T}W(u)[\/latex] rearrange for [latex]T = \\frac{Q}{4\\pi s}W(u)[\/latex]<\/p>\n<\/div>\n

\n

[latex]u\\ = \\frac{r^{2}S}{4Tt}[\/latex] rearrange for [latex]S = \\frac{u\\ 4Tt}{\\ r^{2}}[\/latex]<\/p>\n<\/div>\n

\n

[latex]T\\ = \\ \\frac{0.00347\\frac{{\\ \\ m}^{3}}{s}}{4\\ \\ \\pi\\ \\ 1\\ m}\\ (7)\\ = 0.0019\\ \\frac{{\\ \\ m}^{2}}{s}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

[latex]S = \\ \\frac{0.31\\ (4)\\ 0.0019\\ \\frac{{\\ \\ m}^{2}\\ }{s}\\ 1\\ \\min\\frac{60s\\ }{\\min}}{\\ (150m)^{2}} = 6.4\\ x\\ 10^{- 6}[\/latex]<\/p><\/blockquote>\n<\/div>\n

\n

Return to Exercise\u00a0<\/span><\/a>10<\/u><\/strong>\u2ba5<\/p>\n<\/div>\n

\n

Return to where text linked to Exercise\u00a010<\/strong><\/span><\/a>\u2ba5<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":8,"menu_order":121,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1399","chapter","type-chapter","status-publish","hentry"],"part":1531,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1399","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":4,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1399\/revisions"}],"predecessor-version":[{"id":1880,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1399\/revisions\/1880"}],"part":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/parts\/1531"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapters\/1399\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/media?parent=1399"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/pressbooks\/v2\/chapter-type?post=1399"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/contributor?post=1399"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/basic-hydrogeology-an-introduction-to-the-fundamentals-of-groundwater-science\/wp-json\/wp\/v2\/license?post=1399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}